A Fourier transform technique is described which measures phase delay using short duration pulses or impulses. The method of data analysis is detailed and some simple test functions are used to estimate the accuracy and reliability of the resulting phase delays. It appears that the inherent accuracy associated with this technique is not much different from that of a zero cross-over technique using a chopped CW source and narrowband receiver. The computer software used to fully automate the Fourier transform technique is described. It is clear that the technique can be automated to give reliable measurements of phase delay, which for various reasons is not always possible using the narrowband CW technique. Measurements of ultrasonic phase delays for a 50 mm thick mild steel plate using the Fourier transform technique are given for compressional and shear waves with frequencies around 2 MHz and 5 MHz. Both EMA and piezoelectric transducers have been used. Corresponding measurements of phase delay using a chopped CW stimulus are shown to be in good agreement.